Uniqueness in Rough Almost Complex Structures, and Differential Inequalities

Rosay, Jean-Pierre. "Uniqueness in Rough Almost Complex Structures, and Differential Inequalities." Annales de l’institut Fourier 60.6 (2010): 2261-2273. <http://eudml.org/doc/116332>.

@article{Rosay2010,
abstract = {The study of $J$-holomorphic maps leads to the consideration of the inequations $|\frac\{\partial u\}\{\partial \{\overline\{z\}\}\}|\le C|u|$, and $|\frac\{\partial u\}\{\partial \{\overline\{z\}\}\}| \le \epsilon |\frac\{\partial u\}\{\partial z\}|$. The first inequation is fairly easy to use. The second one, that is relevant to the case of rough structures, is more delicate. The case of $u$ vector valued is strikingly different from the scalar valued case. Unique continuation and isolated zeroes are the main topics under study. One of the results is that, in almost complex structures of Hölder class $\frac\{1\}\{2\}$, any $J$-holomorphic curve that is constant on a non-empty open set, is constant. This is in contrast with immediate examples of non-uniqueness.},
affiliation = {University of Wisconsin Department of Mathematics Madison WI 53705 (USA)},
author = {Rosay, Jean-Pierre},
journal = {Annales de l’institut Fourier},
keywords = {$J$-holomorphic curves; differential inequalities; uniqueness; -holomorphic curves},
language = {eng},
number = {6},
pages = {2261-2273},
publisher = {Association des Annales de l’institut Fourier},
title = {Uniqueness in Rough Almost Complex Structures, and Differential Inequalities},
url = {http://eudml.org/doc/116332},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Rosay, Jean-Pierre
TI - Uniqueness in Rough Almost Complex Structures, and Differential Inequalities
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 6
SP - 2261
EP - 2273
AB - The study of $J$-holomorphic maps leads to the consideration of the inequations $|\frac{\partial u}{\partial {\overline{z}}}|\le C|u|$, and $|\frac{\partial u}{\partial {\overline{z}}}| \le \epsilon |\frac{\partial u}{\partial z}|$. The first inequation is fairly easy to use. The second one, that is relevant to the case of rough structures, is more delicate. The case of $u$ vector valued is strikingly different from the scalar valued case. Unique continuation and isolated zeroes are the main topics under study. One of the results is that, in almost complex structures of Hölder class $\frac{1}{2}$, any $J$-holomorphic curve that is constant on a non-empty open set, is constant. This is in contrast with immediate examples of non-uniqueness.
LA - eng
KW - $J$-holomorphic curves; differential inequalities; uniqueness; -holomorphic curves
UR - http://eudml.org/doc/116332
ER -